Radiation and Ionization Energy Loss Simulation for GDH Sum Rule Experiment in Hall-A at Jefferson Lab
Xin-Hu Yan, Yun-Xiu Ye Jian-Ping Chen, Hai-Jiang LV, Pengjia Zhu, Fengjian Jiang
aa r X i v : . [ phy s i c s . i n s - d e t ] D ec CPC(HEP & NP), 2010, (X): 1—5 Chinese Physics C
Vol. 33, No. X, Xxx, 2010
Radiation and Ionization Energy Loss Simulation for theGDH Sum Rule Experiment in Hall-A at Jefferson Lab * YAN Xin-Hu()
YE Yun-Xiu() CHEN Jian-Ping() LV Hai-Jiang() Zhu Pengjia() Jiang Fengjian() Department of Physics, Huangshan University, Huangshan, Anhui 245041, China Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China Thomas Jefferson National Accelerator Facility, Newport News,VA 23606, USA)
Abstract
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation forthe GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed for C elastic scattering simulation. The relative momentum ratio ∆ pp and C elastic cross section are comparedwithout and with radiative energy loss and a reasonable shape is obtained by the simulation. The total energyloss distribution is obtained, showing a Landau shape for C elastic scattering. This simulation work will givegood support for radiation correction analysis of the GDH sum rule experiment. Key words
GDH sum rule, radiation thickness, ionization, SAMC
PACS
The Gerasimov-Drell-Hearn (GDH) sum rule[1–3] applied to nuclei relates the total cross section ofcircularly polarized photons on a longitudinally po-larized nucleus to the anomalous magnetic momentof the nucleus: Z ∞ thr ( σ A ( ν, Q ) − σ p ( ν, Q )) dνν = − π µ A J (1)where Q = − ( p − p ′ ) is the negative four-momentumsquared of the exchanged photon; p and p ′ are thefour-momenta of the incoming and scattering elec-trons, respectively; σ p and σ A are the total photo-absorption cross sections of the nucleus with nuclearspin J parallel and antiparallel, respectively, to thephoton polarization; and µ A = µ − Jq ¯ h/M is theanomalous magnetic moment of the nucleus, whereq and M are the charge and mass of the nucleus. Thelower limit is the photo-nuclear disintegration thresh-old.In order to obtain precise cross sections from GDHexperiments, radiation correction analysis is impor-tant. In this article, we will discuss a radiation en-ergy loss simulation based on the Single Arm Monte Carlo (SAMC) package for the GDH experiment inHall-A at Jefferson Lab. SAMC is a Monte Carlo package which simulatesone of the two Hall-A HRS (High Resolution Spec-trometers) at Jefferson Lab. In this article, we fo-cus on the Hadron arm (i.e. the left arm in Hall-A).SAMC works by the following procedure. Firstly, thekinematic domain illuminated and the region of in-terest for the analysis are defined in the input files.Secondly, the relevant variables are randomly drawnwith a uniform distribution. All these variables de-fine an event. The event undergoes different checksto see if it reaches the HRS focal plane without be-ing stopped by the various components within thespectrometer. If it passes, the event is reconstructedat the target and stored in the output file. Mean-while, radiation and ionization energy losses are ap-plied each time the electron goes through some mate-rial. Before storing the event, a weight correspondingto the cross section of the event and an asymmetry ∗ Supported by the National Natural Science Foundation of China(11135002,11275083), US Department of Energy contractDE-AC05-84ER-40150 under which Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility andNatural Science Foundation of An’hui Educational Committee(KJ2012B179)1) E-mail: yanxinhu@ mail.ustc.edu.cn c (cid:13) can be assigned. This option is set on or off usingthe input file. Physics can be added into the MonteCarlo results using this weighting factor (cross sec-tion effect) or asymmetry. They are both computedfor each event according to its target reconstructedkinematic quantities. Some physical procedures suchas C elastic cross sctions, radiative corrections andLandau tail for elastic peaks, He quasi-elastic crosssections, asymmetries and external radiation correc-tions can be processed in this simulation package.The physics principle of the SAMC package is sameas the general detector simulation toolkit, Geant4.But the SAMC is more simple, flexible and suitablefor some special simulations of Hall-A at JLab. TheSAMC package has included the forward and back-ward matrix(Optics of the HRSs) to guide the elec-tron to go to the detector plane from the target planefor the HRS. So we can get the simulation results inthe detector plane of HRS in Hall-A at JLab. Thatwill be more useful and efficient for the data analysis.The radiation and ionization energy loss are discussedbelow[4]. The distribution of incident electron energy lossdue to bremsstrahlung in the Coulombic fields of anatom depends on frequency [5–7]. The relation be-tween the energy loss and frequency is expressed asfollows. d E = − hν [ N ] dσ ( ν, E ) dν dxdν (2)where ν is the frequency of radiated photons and [ N ]is the number density of atoms. After integratingover the entire frequency spectrum of radiated pho-tons, the energy distribution of the incident electroncan be expressed as follows when it goes through thematerial: dEE = − [ N ] σ rad dx → E ( x ) = E (0) exp ( − [ N ] σ rad ( Z ) x )(3)where the σ rad ( Z ) depends almost solely on thecharge of the nucleus Z when the incident electronenergies are larger than 50 MeV[8–12]. We can makea assumption that the incident electron can only scat-ter with one atom at a time in uniform material. Un-der this assumption, the total energy loss can be ex-pressed as follows: E ( x ) = E (0) exp ( − X k [ N ] k σ rad ( Z k ) x ) (4)where k represents different types of atomic iso- tope. The radiation length of the material, which isthe thickness needed for an electron to lose 1 − /e ofits initial energy. X represents the radiation lengthin mass per unit “area”: X = AN A σ rad ( Z ) (5)Consequently, the unitless radiation thickness isdefined as: t = ρlX (6)where l is the thickness of the material. When incident electrons are scattered by atomicelectrons in the material, the struck atom can be ion-ized. The mean ionization energy loss per unit massdensity per unit thickness is defined as follows[13]: ï ∆ ρx ò = ï ξρx ò h log ( pcI ) − δ ( X ) + g i (7) ï ξρx ò = ZaAβ (8)where ∆ is the mean ionization energy loss; Z isatomic number; A is the molecular weight of the ma-terial; p is the electron’s momentum; I is the mean ex-citation potential of the material; δ ( X ) is the densitycorrection [14]; and ξ is the “ collisional ” thickness.Since the mean energy loss is given by the Bethe-Bloch equation and the most probable energy loss isgiven by Landau’s energy-loss formula, g can be ex-pressed in different ways[15]. The density correctionparameters from [16] and [17, 18] are used. The sim-ulation will base on the above general methods tocalculate the radiation and ionization energy loss. In order to run the SAMC simulation, we needone physical input file, “C12.inp” which contains thephysics parameters and kinematic domain (i.e. illu-mination area). In this article, we only study C elastic scattering before and after radiative energyloss. For convenience, the description of radiative en-ergy loss will include radiation and ionization energyloss. The main parameters in “C12.inp” are shown inTable 1. o. XYAN Xin-Hu et al:Radiation and Ionization Energy Loss Simulation for GDH Sum Rule Experiment in Hall-A at Jefferson Lab3 Table 1. SAMC Simulation Parameters.Parameters Value Definition N trail E i E p th spec − . ◦ HRS angle dpp ac
5% Relative momentum ∆ pp dth ac
110 mR Vertical angle range dph ac
50 mR Horizontal angle range spot x spot y tgt l ◦ Target polarizationinl 0.00247 g/cm Thickness of mattercrossed by incoming e − outl 0.0199 g/cm Thickness of mattercrossed by scattered e − xdi 0.105 g/cm Thickness of ionizationfor incoming e − xdo 0.798 g/cm Thickness of ionizationfor scattered e − The beam profile is shown in Fig. 1 with a circu-lar raster pattern. The beam size in both the x and ydirections is 0.004 cm. The energy of incoming elec-trons is spread due to the beam energy dispersion.The external bremsstrahlung, ionization and internalbremsstrahlung are then applied. The beam energydispersion is taken as 3 × − . Fig. 1. Beam position and size distribution insimulation.In this simulation, the code treats elastic scatter-ing as different from other physics process such asquasi-elastic scattering, because of the correlation be-tween the scattering angle and the outgoing electronmomentum. In this case, only the scattering angle ischosen randomly. The momentum of the scatteringparticle is then computed according to the angle, themass of the target C and the incoming beam energy. p/p (%) D -1.3 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 E ve n t s Fig. 2. Beam relative momemtum ratio ∆ pp (%)without (solid line) and with (dashed line) radiativeenergy loss at target.Fig. 2 shows the beam relative momentum ra-tio ∆ pp distributions when the beam central momen-tum is equal to 1.14876 GeV/c. The relative momen-tum ratio depends on the different momentum set-tings, and can be tuned by the accelerator. Adjustingthis momentum setting, the solid line shows the rel-ative momentum ratio without radiative energy lossat the target, with the peak at − . ± . − . ± . ∆ pp o. XYAN Xin-Hu et al:Radiation and Ionization Energy Loss Simulation for GDH Sum Rule Experiment in Hall-A at Jefferson Lab4 distribution gets wider after adding the radiative en-ergy loss procedure. barn m C elastic cross section / E ve n t s Fig. 3. C elastic cross section without (solidline) and with (dashed line) radiative energy loss.Fig. 3 shows the C elastic cross section distribu-tion. The solid and dashed lines show the distributionwithout and with radiative energy loss, respectively.From the plot, we can see that the two peaks are bothat around 2869 µbarn . The dashed line is a littlelower than the solid line, but goes a little higher thanthe solid line when the cross section value increasesdue to the radiative energy loss. Total Energy Loss/GeV E ve n t s Fig. 4. Total energy loss distribution includingradiation and ionization energy loss.Fig. 4 shows the total energy loss distribution in-cluding radiation and ionization energy loss. Fromthe plot, we can see that the most probable total en-ergy loss value is around 0 . ± . C elastic cross section vs total energyloss with radiative energy loss.Fig. 5 shows a two dimensional distribution of C elastic cross section versus total energy loss afterthe radiative energy loss procedure. From this plot,we can see that the cross section value increases whenthe total energy loss of particles gets higher, but mostof the events are at lower total energy loss and crosssection value.The above results are from SAMC simulation for C elastic scattering without and with radiative en-ergy loss. We have included internal radiation (vac-uum polarization, vertex corrections) energy loss andexternal radiation (ionization and bremsstrahlung)energy loss. These simulation results can be com-pared with the C elastic data of the GDH sum ruleexperiment in future. If the simulation results matchthe elastic data well, this will show the good state ofthe data quality. The radiative corrections take thegeneral form σ exp = (1 + δ ) σ Born where the δ repre-sents the sum of the internal and external radiativecorrections. We can make a comparison between thedata and the physical theory after finishing cross sec-tion analysis. This simulation work will be helpful forthe above data analysis. This article studied the radiation and ionizationenergy loss based on single arm Monte Carlo simula-tion for the GDH sum rule experiment in Hall-A atJefferson Lab. The radiation and ionization energyloss were discussed for C elastic scattering simula-tion. The relative momentum ratio ∆ pp and C elasticcross section were compared without and with radia-tive energy loss and a reasonable shape was obtainedby the simulation. The total energy loss (includingradiation and ionization) distribution was obtained, o. XYAN Xin-Hu et al:Radiation and Ionization Energy Loss Simulation for GDH Sum Rule Experiment in Hall-A at Jefferson Lab5 giving a reasonable distribution with a Landau shapefor C elastic scattering. This simulation work willprovide good support for radiation correction analysisof the GDH sum rule experiment. We would like to thank J.P. Chen for his sugges-tions and discussion, and J. Singh and V. Sulkoskyfor their help.